4. A motorcar of mass 1200 kg is moving along a straight line with a uniform velocity of 90 km h'. Its velocity is slowed down to 18 km h in 4 s by an unbalanced external force. Calculate the acceleration and change in momentum. Also calculate the magnitude of the force required.
Answers
Answer : Acceleration (a) = -5m/s²
Change in momentum = -24000 kgm/s
Force = 6000 N
Step-by-step explanation:
Given: mass of motorcycle (m)= 1200 kg,
initial velocity of motorcycle (u) = 90 km/h
= 90 x 1000 / 60 × 60 = 25 m/s
final velocity of motorcycle (v) = 18 km/h
= 18 x 1000 / 60 × 60 = 5 m/s
and time taken ( t ) = 4 s
To find: Acceleration, change in momentum and the magnitude of the
force required
We know that, acceleration (a) = v - u / t
(a) = 5 - 25 / 4
= - 5 m/s² ( Negative sign shows that the motorcar is retarted or decelerated)
Now, change in momentum = m(v – u) = 1200 ( 5 - 25 )
= 1200 × (-20)
= -24000 kg m/s (Negative sign shows that the momentum is decreasing).
Magnitude of the force required, F = ma = 1200 x 5 = 6000 N.