Practice Instantaneous Speed in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Instantaneous speed is the speed of an object at a particular moment in time.

It is what a speedometer shows right now, not over the whole trip.

Showing a random 20 of 50 problems.

Example 1

medium

Position is

x(t) = 4t - t^2

m. Find the time when instantaneous speed is zero (slope

4 - 2t

Example 2

easy

Position is

x(t)=4t

m. What is the instantaneous speed at

t=2

Example 3

easy

A car at constant acceleration starts from rest and reaches

30 \text{ m/s}

6 \text{ s}

. Find its instantaneous speed at

t=3 \text{ s}

Example 4

easy

Is instantaneous speed a scalar or a vector?

Example 5

medium

A position-time graph shows a curve whose slope at

t=4 \text{ s}

-3

(m per s). Find the instantaneous speed at

t=4 \text{ s}

Example 6

challenge

Position is

x(t)=t^3

m. Find the instantaneous speed at

t=2

s (slope is

3t^2

Example 7

medium

A position-time graph is a straight line through the origin with slope

7

. What is the instantaneous speed?

Example 8

easy

Over a whole trip a car's average speed is

50

km/h. Must its instantaneous speed always be

50

km/h?

Example 9

medium

Position is

x(t)=t^2

m. Estimate the instantaneous speed at

t=3

s using the slope

2t

Example 10

medium

Between

t=1

s and

t=1.01

s an object moves

0.0

0.0

... actually from

2.00

m to

2.06

m. Estimate the instantaneous speed near

t=1

Example 11

hard

A particle's velocity-time graph is a triangle:

v=0

t=0

, peaks at

v=12 \text{ m/s}

t=3 \text{ s}

, drops linearly back to

v=0

t=6 \text{ s}

. Find its instantaneous speed at

t = 2 \text{ s}

Example 12

easy

A speedometer reads

80 \text{ km/h}

right now. Is this instantaneous or average speed?

Example 13

challenge

Position is

x(t)=5t-t^2

m. At what time is the instantaneous speed zero (slope

5-2t

Example 14

medium

An object's average speed over an interval is

4 \text{ m/s}

. Can its instantaneous speed at some moment in that interval be

0 \text{ m/s}

Example 15

easy

An object moves

20 \text{ m}

4 \text{ s}

at constant speed. Find its instantaneous speed at

t = 2 \text{ s}

Example 16

medium

Between

t=5 \text{ s}

and

t=5.01 \text{ s}

a runner moves from

30.00 \text{ m}

30.07 \text{ m}

. Estimate the instantaneous speed near

t=5 \text{ s}

Example 17

medium

A car decelerates from

20 \text{ m/s}

at constant

a = -2 \text{ m/s}^2

. Find its instantaneous speed at

t = 6 \text{ s}

Example 18

easy

A speedometer reads

25

m/s right now. What kind of speed is this?

Example 19

hard

x(t) = 2t + \sin(t)

m. Estimate the instantaneous speed at

t = 0

s using the slope

2 + \cos(t)

Example 20

medium

Is instantaneous speed always positive, always negative, or can it be either?

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Related Concepts

Velocity Average Speed