A car is traveling at 16 m/s. It begins to slow with an acceleration of a = (-1/2)t. How far has it traveled by the time t= 4s?

Question

I am aware that you cannot use kinematic equations for this problem because acceleration is not constant. This is why I am confused on how to solve this problem. I know the answer is 59, but how do you get this answer?

Answer 1

Since the acceleration is not constant, you may need to use calculus.

 

a(t) = -t/2

 

v(t) = ∫a(t)dt = -t²/4 + v(0)

 

v(0) = 16 m/s  [given]

 

v(t) = 16 - t²/4

 

x(t) = ∫v(t)dt = 16t - t³/12 + x(0)

 

We do not know x(0), but the distance traveled is x(t) - x(0).

 

x(t) - x(0) = 16t - t³/12

 

x(4) - x(0) = 16(4) - (4)³/12 ≅ 58.67 ≅ 59

 

It travels approximately 59 m is 4 seconds.