Answer:
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
Answer:
(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
