Question

A car starts from rest and accelerates at 4 m/s^2 for 8 s, after which it continues at constant speed for 19 s. How far would it have traveled from its starting point by that time.

Answer 1

The total distance traveled is 736 m

Solution:

According to the question:

Initial velocity, v = 0

(since, the car is starting from rest)

`acceleration, a = 4 m/s^(2)`

Time taken, t = 8 s

Now, the distance covered by it in 8 s is given by the second eqn of motion:

`d = vt + \farc{1}{2}at^(2)`

`d = 0.t + \farc{1}{2}4* 8^(2) = 128 m`

Now, to calculate the velocity, we use eqn 1 of motion:

v' = v + at

v' = 0 + 4(8) = 32 m/s

Now, the distance traveled by the car with uniform velocity of 32 m/s for t' = 19 s:

distance, d' = v't'

`d' = 32* 19 = 608 m`

Total distance traveled = d + d' = 128 + 608 = 736 m