This page answers selected Physics Questions under Linear Motion, backed up with correct Workings and Solutions. Generally, Linear Motion can be defined as motion along a straight path. In other to solve reasonable problems correctly under this topic. You must be vast with equations of Motion.

Equation of Uniformly accelerated Motion

• v = u + at
• v ² = u² +2as
• s = ut +1/2at²
• s = ((v+u)/2) x t

v= final Velocity; u = initial velocity; s = distance or displacement and t = time

Question 1: A car accelerates uniformly from rest at 3m/s²  its velocity after traveling a distance of 24m is A. 144m/s B. 72m/s C. 36m/s D. 12m/s

Answer is D

Solution: From the question we were given the following; u (initial velocity) = 0; because it starts from rest; acceleration a = 3m/s²  , distance s = 24m. we are looking for final velocity v = ?

We are going to use the equation of motion; v ² = u² +2as (Note: check your parameters given to determine the needed equation.

v ² = 0 + 2*3*24

= 144;

v = √144 = 12m/s (Solved)

Question 2: A car starts from rest and moves with a uniform acceleration of 30m/s² for 20s.Calculate the distance covered at the end of the motion. A. 6km. B. 12km. C. 18km. D. 24km. (2012/7)

Answer is A

Solution: We were given; initial velocity u = 0 ( because it starts from rest); acceleration a = 30m/s² and time t = 20seconds; we are looking for distance.

From the parameters given, the most suitable equation of motion to use is; s = ut +1/2at²

s = 0*20 + 1/2 * 30 * (20)²

= 0 + 15*400

s = 6000m; Since the answer is in kilometer (km) since 1000m = 1km; then 6000m = 6km (solved)

Question 3: The velocity v of a particle in a time t is given by the equation v = 10 + 2t². find the instantaneous acceleration after 5 seconds.  A. 10m/s² B. 15m/s² C. 20m/s² D. 60m/s² (2000/8)

Answer is C

Solution: differentiation of distance or displacement (s) with respect to time (t) will give us velocity (v) and the derivation of velocity (v) with respect to time (t) will give us acceleration

i.e from your mathematics, ds/dt = v and dv/dt = a; refer to your mathematics (calculus)

From the question, v = 10 + 2t² ; dv/dt = a = 2*2t^2-1

a = 4t; since t = 5 seconds from the question; a = 4*5 = 20m/s² (Solved)

Question 4: Abody falls freely under gravity (g = 9.8m/s²) from a height of 40m on the top of a platform 0.8m above the ground. Its velocity on reaching the platform is A. 784m/s B. 80m/s C. 78.4m/s D. 27.7m/s (1981/33).

Answer is D

Solution: Since the object falls (downward motion) acceleration due to gravity (g) will be positive and it is given as 9.8m/s²  ; initial velocity u = 0 (When an object falls from a height the initial velocity will be zero) ; distance (s) = 40m – 0.8m = 39.2m and you are to find final velocity (v)

v ² = u² +2as

v ²= 0 + 2*9.8*39.2

v ² = 768.32; v = √768.32

v= 27.7m/s (solved).

Class work: A car accelerates uniformly from rest at 4m/s². How far will it travel in the fifth complete second? A. 100. B. 50m. C. 32m. D. 18m. (2009/5).

Assignnments

1. A car travels along a straight road at a constant speed of 60 km/h for 2 hours. What is the total distance traveled by the car?
2. An object is dropped from a height of 80 meters. Ignoring air resistance, how long will it take for the object to reach the ground?
3. An automobile accelerates from rest at a rate of 2 m/s^2 for 5 seconds. What is the final velocity of the cyclist?
4. A train travels from one station to another, covering a distance of 500 km in 4 hours. What is the average speed of the train?
5. A ball is thrown vertically upward with an initial velocity of 20 m/s. How high will the ball go before it starts falling back down?

Essay Questions

1. Define linear motion and provide an example from everyday life.
2. Explain the difference between speed and velocity in the context of linear motion.
3. Discuss the concept of acceleration and provide examples of situations where an object undergoes acceleration.
4. Describe the motion of an object with a constant velocity and explain how it differs from an object with a changing velocity.
5. Discuss the factors that can affect the motion of an object, such as friction, air resistance, and gravitational force.

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I believe you have a better understanding of Linear Motions Now. Kindly drop any questions you are having issues with in the comment section below. We will solve it.!!!