A car is moving 14.4 m/s when it hits the brakes. It slows for 78.8 m, which takes 9.92 s. It then accelerates at 1.83 m/s^2 for 4.50 s. What is its final velocity?

2-part motion

1-D kinematics

This is a 2-part motion.

Part 1 of the motion:

Applying equations of motion;

u = 14.4 m/s, s = 78.8 m, t = 9.92 s

s = ut+1/2at^2

78.8 = 14.4*9.92 + 1/2*a*9.92^2

78.8 = 142.848 + 49.2032a

a = (78.8-142.848) / 49.2032 = - 1.3 m/s^2 (negative sign indicates a deceleration).

Now,

v = u+at

v = 14.4 - 1.3*9.92 = 1.49 m/s

Part 2 of the motion:

Final speed in first motion becomes initial velocity in this second motion.

u = 1.49 m/s, a = 1.83 m/s^2, t = 4.50 s

Now,

v = u + at

Then,

v = 1.49 + 1.83*4.50 = 9.72 m/s

The final speed is 9.72 m/s