Suppose a child drives a bumper car head on into the side rail, which exerts a force of 3400 N on the car for 0.400 s. (a) What impulse (in kg · m/s) is imparted by this force? (b) Find the final velocity (in m/s) of the bumper car if its initial velocity was 3.20 m/s and the car plus driver have a mass of 200 kg. You may neglect friction between the car and floor.

a) 1360kgm/s b) 5.14m/s

Explanation:

a) According to Newton's second law of motion,

Force = mass * acceleration

F = ma

since acceleration = change in velocity (v-u) / time (t)

F = m (v-u) / t

Ft = m (v-u) = Impulse.

Impulse is defined as change in momentum of a body. It can be expressed as;

Impulse = Ft = m (v-u)

Given force exerted on the car = 3400N

time taken = 0.400seconds

Impulse = 3400*0.4

Impulse = 1360kgm/s

b) To find the final velocity / (v) of the car, we will use the equation of motion below;

v = u+at where;

v is the final velocity = ?

u is the initial velocity = 3.2m/s

a is the acceleration

t is the time taken = 0.4second

To get the acceleration, we will use the formula F = ma where;

m is the mass

F is the force

a is the acceleration

a = F/m = 3400/200

a = 17m/s²

Substituting the values to get the final velocity 'v' we have;

v² = 3.2²+17 (0.4)

v² = 10.24+6.8

v² = 17.04

v = √17.04

v = 4.13m/s

The final velocity of the bumper car is 4.14m/s

(a) 1360 Ns

(b) 10 m/s

Explanation:

(a)

Impulse: This can be defined as the product of force and time. The S. I unit of impulse is Ns

From Newton's third law,

The expression for impulse is given as,

I = F*t ... Equation 1

Where I = Impulse, F = Force, t = Time.

Given: F = 3400 N, t = 0.4 s

Substitute into equation 1

I = 3400*0.4

I = 1360 Ns

(b)

From newton third law of motion,

Impulse = Change in momentum.

I = m (v-u) ... Equation 2

Where I = impulse, m = mass of the car plus the driver, v = final velocity of the bumper car, u = initial velocity of the car.

make v the subject of the equation

v = (I/m) + u ... Equation 3

Given: I = 1360 Ns, m = 200 kg, u = 3.2 m/s

Substitute into equation 3

v = (1360/200) + 3.2

v = 6.8+3.2

v = 10 m/s