Practice – Solve problems involving acceleration

Questions :

In the following questions, take moving to the right as positive.

1. You are moving to the left and you are slowing down. What is the sign of your velocity and acceleration?
2. You are moving to the right and you are speeding up. What is the sign of your velocity and acceleration?
3. You are moving to the left and speeding up. What is the sign of your velocity and acceleration?
4. You are moving to the right and slowing down. What is the sign of your velocity and acceleration?

You were driving east with an average velocity of 30 km/hr. In 30 min you increased your velocity at a constant rate to 60 km/hr. What is your acceleration? What does the sign of acceleration tell you?

You were driving West with an average velocity of 50 km/hr. In 2 hrs you came to a stop. What is your acceleration? What does the sign of acceleration tell you? ( Take East as the positive side)

A runner started running from a stop position. He got a velocity of  ( Take East as the positive side) 2m/s in 30 min. What is his acceleration?

A driver was driving at an average velocity of 20 m/s. After 30 min his speed was 80 km/hr. Assuming uniformly increased velocity what is the acceleration of the car ( in m/s²)?

Explanations :

In the following questions, take moving to the right as positive.

You are moving to the left and you are slowing down. What is the sign of your velocity and acceleration?

Velocity is negative and acceleration is positive.

2. You are moving to the right and you are speeding up. What is the sign of your velocity and acceleration?

Velocity is positive and acceleration is positive.

3. You are moving to the left and speeding up. What is the sign of your velocity and acceleration?

Velocity is negative and acceleration is negative.

4. You are moving to the right and slowing down. What is the sign of your velocity and acceleration?

Velocity is positive and acceleration is negative.

You were driving east with an average velocity of 30 km/hr. In 30 min you increased your velocity at a constant rate to 60 km/hr. What is your acceleration? What does the sign of acceleration tell you?

Average acceleration = ( Change in velocity) / ( Time)

Change in velocity = 60 km – 30 km = 30 km

Time = 30 min = 0.5 hr

Average acceleration = (30 km/hr) / (0.5 hr) = 60 km/hr²

Velocity and acceleration have the same sign. That means I am speeding up.

You were driving West with an average velocity of 50 km/hr. In 2 hrs you came to a stop. What is your acceleration? What does the sign of acceleration tell you? ( Take East as the positive side)

Average acceleration = ( Change in velocity) / ( Time)

Change in velocity = (Final Velocity) – ( Starting Velocity )

[Final velocity = 0 ( you came to stop)

Starting velocity = -50 km/hr ( East is positive so west is negative)]

Change in velocity = 0 – (-50) km/hr = 50 km/hr

Time = 2 hrs.

Average acceleration = (50 km/hr) / (2 hr) = 25 km/hr²

In this case, velocity is negative but acceleration is positive. That means you are slowing down but still moving in a negative direction.

A runner started running towards East from a stop position. He got a velocity of   2m/s in 30 min. What is his acceleration?( Take East as the positive side)

Average acceleration = ( Change in velocity) / ( Time)

Change in velocity = (Final Velocity) – ( Starting Velocity )

[Final velocity = 2 m/s

Starting velocity = 0 m/s ]

Change in velocity = 2 – 0 m/s = 2 m/s

Time = 30 min = 1800 s

Average acceleration = (2 m/s) / (1800 s) = 0.0011 m/s²

A driver was driving at an average velocity of 20 m/s. After 30 min his speed was 80 km/hr. Assuming uniformly increased velocity what is the acceleration of the car ( in m/s²?

• Make sure all units are same

Average acceleration = ( Change in velocity) / ( Time)

Change in velocity = (Final Velocity) – ( Starting Velocity )

[Final velocity = 80 km/hr = 80000 m / 3600 s = 22.22 m/s

Starting velocity = 20 m/s ]

Change in velocity = 22.22 – 20 m/s = 2.22 m/s

Time = 30 min = 1800 s

Average acceleration = (2.22 m/s) / (1800 s) = 0.0012 m/s²

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