Answer to Question #301215 in Physics for Lei

Question

A car is moving at uniform acceleration. Its velocity after traveling for 2 seconds is 4m/s

and is found 12 meters from where it started. If the car’s velocity at 5 seconds is 10 m/s,

determine (a) the car’s acceleration, (b) its displacement at t = 5 seconds measured

from its starting point and (c) its velocity at the start.

Answer 1

The distance traveled by a car

$$d=\frac{v_i+v_f}{2}t$$

The initial speed

$$v_i=2d/t-v_f=2*12/2-4=8\:\rm m/s$$

The acceleration

$$a=\frac{v_f-v_i}{t}=\frac{4-8}{2}=-2\:\rm m/s^2$$

The displacement for the 5 sec

$$d=v_it+at^2/2=8*5+(-2)*5^2/2=15\:\rm m$$