Question

A Smart Car, which has a mass of 1000 kg, is going 20 m/s. When it hits the barrier, it stops at a time of 0.5 seconds. What is the impulse on the car?

Answer 1

Imp = 20000 [kg*m/s]

Step-by-step explanation:

In order to solve this problem we must divide it into two parts. In the first part we must use the following equation of kinematics.

`V_(f)=v_(i)-a*t`

where:

Vf = final velocity = 0 (the car stops)

Vi = initial velocity = 20 [m/s]

a = acceleration [m/s²]

t = time = 0.5 [s]

Acceleration is negative as the cart slows down as it stops.

`0=20-a*0.5\\20=0.5*a\\a=40 [m/s^(2)]`

The second part is the determination of momentum, which is defined as the product of force over a given time. But to determine the force we must use Newton's second law which tells us that the sum of the forces of a body is equal to the product of mass by acceleration.

∑F = m*a

`F = 1000*40\\F = 40000[N]`

Now the impulse or momentum

`Imp = F*t\\Imp = 40000*0.5\\Imp=20000[kg*m/s]`