Motion in a Straight Line — Practice

Question 1

A particle moves with v = 10 + 2t m/s. Find the displacement from t = 0 to t = 5 s.

Accepted Answer

s = integral of v dt = integral(10 + 2t)dt = 10t + t^2, evaluated 0 to 5 = 50 + 25 = 75 m.

Question 2

A car moving at 72 km/h stops in 50 m. Find the deceleration.

Accepted Answer

u = 20 m/s. v^2 = u^2 + 2as: 0 = 400 + 2a(50), so a = -4 m/s^2.

Question 3

Two 100 m trains move at 54 km/h and 72 km/h in opposite directions on parallel tracks. Find the crossing time.

Accepted Answer

Relative speed = 54 + 72 = 126 km/h = 35 m/s. Total distance = 200 m. Time = 200/35 = 5.71 s.

Question 4

A stone is dropped from an 80 m tower. Find the time to reach the ground and the impact speed (g = 10 m/s^2).

Accepted Answer

s = (1/2)g t^2: 80 = 5 t^2, so t = 4 s. Impact speed v = g t = 40 m/s.

Question 5

Can an object have zero velocity but non-zero acceleration? Give an example.

Accepted Answer

Yes. At the highest point of a ball thrown vertically upward, the velocity is momentarily zero, but the acceleration is g = 9.8 m/s^2 downward.

Practice — Motion in a Straight Line