The acceleration of the bus is 1.11 meters per second square to the direction of motion
Explanation:
Acceleration is the rate of change of velocity
The formula of the acceleration is
, where
is the initial velocity
is the final velocity- t is the time
A bus that goes from 10 km/h to a speed of 50 km/h in 10 seconds
→
= 10 km/h
→
= 50 km/h
→ t = 10 seconds
Change the unite of the time from seconds to hour
→ 1 hour = 60 × 60 = 3600 seconds
→ 10 seconds =
hour
Substitute these values in the formula of the acceleration above
→ 
→ a = 14400 km/h²
To change the unit of acceleration to meter per second change the
kilometer to meter and the hour to seconds
→ 1 km = 1000 m
→ 1 hour = 3600 seconds
→ 
→ a = 1.11 m/sec².
The acceleration of the bus is 1.11 meters per second square to the direction of motion
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Answers:
a) 
b) 
Explanation:
a) The centripetal acceleration
of an object moving in a uniform circular motion is given by the following equation:
Where:
is the angular velocity of the ball
is the radius of the circular motion, which is equal to the length of the string
Then:
This is the centripetal acceleration of the ball
b) On the other hand, in this circular motion there is a force (centripetal force
) that is directed towards the center and is equal to the tension (
) in the string:

Where
is the mass of the ball
Hence:

This is the tension in the string
a) 32 kg m/s
Assuming the spring is initially at rest, the total momentum of the system before the collision is given only by the momentum of the bowling ball:

The ball bounces off at the same speed had before, but the new velocity has a negative sign (since the direction is opposite to the initial direction). So, the new momentum of the ball is:

The final momentum after the collision is the sum of the momenta of the ball and off the spring:

where
is the momentum of the spring. For the conservation of momentum,

b) -32 kg m/s
The change in momentum of bowling ball is given by the difference between its final momentum and initial momentum:

c) 64 N
The change in momentum is equal to the product between the average force and the time of the interaction:

Since we know
, we can find the magnitude of the force:

The negative sign simply means that the direction of the force is opposite to the initial direction of the ball.
d) The force calculated in the previous step (64 N) is larger than the force of 32 N.
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The answer is X. I hope this helped