Kinematics Study Materials for Competitive Exams

Kinematics

Motion in One Dimension Motion in Two Dimensions Relative Motion

Q. A ball is dropped from a height of 80 m. How long will it take to reach the ground?

A. 4 s
B. 5 s
C. 6 s
D. 8 s

Solution

Using the formula: h = 0.5 * g * t², where h = 80 m and g = 9.8 m/s². Rearranging gives t² = (2 * h) / g = (2 * 80) / 9.8 ≈ 16.33, so t ≈ 4.03 s.

Correct Answer: C — 6 s

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Q. A ball is dropped from a height of 80 m. How long will it take to reach the ground? (Assume g = 10 m/s²)

A. 4 s
B. 5 s
C. 6 s
D. 8 s

Solution

Using the formula: h = 0.5 * g * t^2. 80 = 0.5 * 10 * t^2. Solving gives t^2 = 16, so t = 4 s.

Correct Answer: B — 5 s

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Q. A ball is thrown at an angle of 30 degrees with a speed of 30 m/s. What is the time of flight until it hits the ground?

A. 3 s
B. 4 s
C. 5 s
D. 6 s

Solution

Time of flight (T) = (2u * sin(θ))/g = (2 * 30 * 0.5)/9.8 ≈ 3.06 s.

Correct Answer: C — 5 s

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Q. A ball is thrown at an angle of 30 degrees with an initial speed of 25 m/s. What is the time to reach the maximum height?

A. 1.25 s
B. 2.5 s
C. 3.5 s
D. 5 s

Solution

Time to max height t = (u * sin(θ)) / g = (25 * (1/2)) / 9.8 ≈ 1.28 s.

Correct Answer: B — 2.5 s

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Q. A ball is thrown at an angle of 45 degrees with an initial speed of 14 m/s. What is the range of the projectile?

A. 10 m
B. 14 m
C. 20 m
D. 28 m

Solution

Range (R) = (u² * sin(2θ)) / g = (14² * 1) / 9.8 ≈ 20 m.

Correct Answer: D — 28 m

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Q. A ball is thrown at an angle of 45 degrees with an initial speed of 28 m/s. What is the vertical component of the velocity at the peak of its trajectory?

A. 0 m/s
B. 14 m/s
C. 20 m/s
D. 28 m/s

Solution

At the peak, the vertical component of velocity is 0 m/s.

Correct Answer: A — 0 m/s

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Q. A ball is thrown at an angle of 60 degrees with a speed of 15 m/s. What is the horizontal range of the ball?

A. 20 m
B. 30 m
C. 40 m
D. 50 m

Solution

Range (R) = (u^2 * sin(2θ)) / g = (15^2 * sin(120)) / 9.8 = 38.5 m.

Correct Answer: C — 40 m

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Q. A ball is thrown downward with an initial speed of 10 m/s from a height of 20 m. How long will it take to hit the ground? (g = 10 m/s²)

A. 2 s
B. 3 s
C. 4 s
D. 5 s

Solution

Using the equation of motion: h = ut + 0.5gt². 20 = 10t + 0.5 * 10 * t². Rearranging gives 5t² + 10t - 20 = 0. Solving this quadratic gives t = 2 s.

Correct Answer: B — 3 s

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Q. A ball is thrown downward with an initial speed of 10 m/s from a height of 20 m. How long will it take to hit the ground? (Assume g = 10 m/s²)

A. 2 s
B. 3 s
C. 4 s
D. 5 s

Solution

Using the equation of motion: h = ut + 0.5gt². 20 = 10t + 0.5 * 10 * t². Rearranging gives 5t² + 10t - 20 = 0. Solving this quadratic gives t = 2 s.

Correct Answer: C — 4 s

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Q. A ball is thrown downward with an initial speed of 5 m/s from a height of 20 m. How long will it take to hit the ground? (g = 10 m/s²)

A. 2 s
B. 3 s
C. 4 s
D. 5 s

Solution

Using the equation of motion: h = ut + 0.5gt². 20 = 5t + 0.5 * 10 * t². Rearranging gives 5t + 5t² - 20 = 0. Solving the quadratic gives t = 2 s.

Correct Answer: B — 3 s

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Q. A ball is thrown downwards with an initial velocity of 5 m/s from a height of 20 m. How long will it take to hit the ground? (g = 10 m/s²)

A. 2 s
B. 3 s
C. 4 s
D. 5 s

Solution

Using the equation of motion: h = ut + 0.5gt². 20 = 5t + 0.5 * 10 * t². This simplifies to 5t + 5t² - 20 = 0. Solving gives t = 2 s.

Correct Answer: B — 3 s

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Q. A ball is thrown horizontally from the top of a cliff 45 m high. How far from the base of the cliff will it land if it is thrown with a speed of 10 m/s?

A. 20 m
B. 30 m
C. 40 m
D. 50 m

Solution

Time to fall = sqrt(2h/g) = sqrt(2*45/9.8) ≈ 3.03 s. Horizontal distance = speed * time = 10 * 3.03 ≈ 30.3 m, approximately 30 m.

Correct Answer: B — 30 m

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Q. A ball is thrown horizontally from the top of a cliff 80 m high. How far from the base of the cliff will it land? (Assume g = 10 m/s² and horizontal speed = 20 m/s)

A. 20 m
B. 40 m
C. 60 m
D. 80 m

Solution

Time to fall = √(2h/g) = √(2*80/10) = 4 s. Horizontal distance = speed * time = 20 m/s * 4 s = 80 m.

Correct Answer: C — 60 m

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Q. A ball is thrown horizontally from the top of a cliff 80 m high. How far from the base of the cliff will it land? (Assume g = 10 m/s² and initial horizontal speed = 20 m/s)

A. 40 m
B. 60 m
C. 80 m
D. 100 m

Solution

Time to fall = √(2h/g) = √(2*80/10) = 4 s. Horizontal distance = speed * time = 20 * 4 = 80 m.

Correct Answer: C — 80 m

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Q. A ball is thrown horizontally from the top of a cliff with a speed of 15 m/s. If the cliff is 45 m high, how far from the base of the cliff will the ball land?

A. 30 m
B. 45 m
C. 60 m
D. 75 m

Solution

Time to fall = √(2h/g) = √(2*45/10) = 3 s. Horizontal distance = speed * time = 15 m/s * 3 s = 45 m.

Correct Answer: C — 60 m

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Q. A ball is thrown upwards with a speed of 20 m/s. How high will it go before it starts to fall back?

A. 10 m
B. 20 m
C. 30 m
D. 40 m

Solution

Maximum height H = (u²)/(2g) = (20²)/(2 * 9.8) ≈ 20.4 m.

Correct Answer: B — 20 m

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Q. A ball is thrown upwards with a speed of 20 m/s. How high will it rise before coming to a stop?

A. 10 m
B. 20 m
C. 30 m
D. 40 m

Solution

Maximum height (H) = (u²)/(2g) = (20²)/(2*9.8) ≈ 20.4 m.

Correct Answer: C — 30 m

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Q. A ball is thrown upwards with a speed of 20 m/s. How high will it rise before coming to rest?

A. 10 m
B. 20 m
C. 30 m
D. 40 m

Solution

Maximum height (H) = (u²)/(2g) = (20²)/(2*9.8) ≈ 20.4 m.

Correct Answer: B — 20 m

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Q. A ball is thrown upwards with a speed of 20 m/s. How long will it take to reach the maximum height?

A. 2 s
B. 3 s
C. 4 s
D. 5 s

Solution

Time to reach maximum height (t) = u/g = 20/9.8 ≈ 2.04 s.

Correct Answer: A — 2 s

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Q. A ball is thrown vertically upwards with a speed of 30 m/s. How high will it rise before coming to rest momentarily?

A. 45 m
B. 30 m
C. 60 m
D. 75 m

Solution

Using the equation v² = u² + 2as, where v = 0, u = 30 m/s, and a = -9.8 m/s² (acceleration due to gravity), we have 0 = (30)² + 2*(-9.8)*s. Solving gives s = 45.92 m, approximately 45 m.

Correct Answer: A — 45 m

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Q. A boat can row at 5 km/h in still water. If it takes 2 hours to row upstream against a current, how far has it traveled?

A. 5 km
B. 10 km
C. 15 km
D. 20 km

Solution

Distance = speed × time. Upstream speed = 5 - current speed. If current speed is 1 km/h, distance = (5 - 1) × 2 = 8 km.

Correct Answer: B — 10 km

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Q. A boat can travel at 10 km/h in still water. If it is moving downstream in a river flowing at 5 km/h, what is the speed of the boat relative to the riverbank?

A. 5 km/h
B. 10 km/h
C. 15 km/h
D. 20 km/h

Solution

Speed downstream = Speed of boat + Speed of river = 10 km/h + 5 km/h = 15 km/h.

Correct Answer: C — 15 km/h

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Q. A boat can travel at 10 km/h in still water. If the current flows at 2 km/h, what is the speed of the boat downstream?

A. 8 km/h
B. 10 km/h
C. 12 km/h
D. 14 km/h

Solution

Speed downstream = speed of boat + speed of current = 10 + 2 = 12 km/h.

Correct Answer: C — 12 km/h

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Q. A boat can travel at 10 km/h in still water. If the current of the river is 2 km/h, what is the speed of the boat downstream?

A. 8 km/h
B. 10 km/h
C. 12 km/h
D. 14 km/h

Solution

Speed downstream = speed of boat + speed of current = 10 + 2 = 12 km/h.

Correct Answer: C — 12 km/h

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Q. A boat can travel at 12 km/h in still water. If it is going downstream in a river flowing at 3 km/h, what is the speed of the boat relative to the riverbank?

A. 9 km/h
B. 12 km/h
C. 15 km/h
D. 3 km/h

Solution

Speed of boat downstream = Speed of boat + Speed of river = 12 km/h + 3 km/h = 15 km/h.

Correct Answer: C — 15 km/h

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Q. A boat can travel at 12 km/h in still water. If it is going downstream in a river flowing at 4 km/h, what is the speed of the boat relative to the riverbank?

A. 8 km/h
B. 12 km/h
C. 16 km/h
D. 20 km/h

Solution

Speed of boat downstream = Speed of boat + Speed of river = 12 km/h + 4 km/h = 16 km/h.

Correct Answer: C — 16 km/h

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Q. A boat can travel at 12 km/h in still water. If it is moving downstream in a river flowing at 4 km/h, what is the speed of the boat relative to the riverbank?

A. 8 km/h
B. 12 km/h
C. 16 km/h
D. 4 km/h

Solution

Speed of boat relative to riverbank = Speed of boat + Speed of river = 12 km/h + 4 km/h = 16 km/h.

Correct Answer: C — 16 km/h

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Q. A boat can travel at 12 km/h in still water. If it travels downstream in a river flowing at 3 km/h, what is its speed relative to the riverbank?

A. 9 km/h
B. 12 km/h
C. 15 km/h
D. 18 km/h

Solution

Speed downstream = Speed of boat + Speed of river = 12 km/h + 3 km/h = 15 km/h.

Correct Answer: C — 15 km/h

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Q. A boat can travel at 15 km/h in still water. If it takes 2 hours to go upstream and 1 hour to return downstream, what is the speed of the current?

A. 3 km/h
B. 4 km/h
C. 5 km/h
D. 6 km/h

Solution

Let speed of current = x. Upstream speed = 15 - x, Downstream speed = 15 + x. Distance = speed × time. 2(15 - x) = 1(15 + x). Solving gives x = 5 km/h.

Correct Answer: C — 5 km/h

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Q. A boat can travel at 15 km/h in still water. If it takes 2 hours to travel upstream and 1.5 hours to travel downstream, what is the speed of the current?

A. 2 km/h
B. 3 km/h
C. 4 km/h
D. 5 km/h

Solution

Let speed of current = x. Upstream speed = 15 - x, Downstream speed = 15 + x. (2 hours)(15 - x) = (1.5 hours)(15 + x). Solving gives x = 3 km/h.

Correct Answer: B — 3 km/h

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Kinematics

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