A car starts from rest and moves along the x-axis with constant acceleration 5 m s–2 for 8 seconds. If it then continues with constant velocity, what distance will the car cover in 12 seconds since it started from the rest?

Question

A car starts from rest and moves along the x-axis with constant acceleration 5 m s&#x2013;2 for 8 seconds. If it then continues with constant velocity, what distance will the car cover in 12 seconds since it started from the rest?

Philoid · Accepted Answer

As the car moves from rest, where u = 0,

Acceleration, a = 5ms^-2

time, t = 8sec

distance(s) =?

From the equation of motion

S₁ = ut + 1/2 at²

S₁ = (0x8) + 1/2 x 5 x (8)²

S₁ = 0 +1/2x5x64

S₁ = 5x32

S₁ =160 m

The velocity after 8 sec,

From equation of motion

v = u + at

v = 0 + 5 x 8

v = 40m/s

So, the distance travelled in 4 sec (12 s – 8 s = 4s)

S₂ = 40 x 4

S₂ = 160 m

Therefore, total distance travelled by the car = S₁ + S₂

= 160 + 160

= 320 m