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Calculus

Displacement, Velocity, Acceleration

Concept Quizzes

Average Velocity
Instantaneous Velocity
Finding Acceleration Given Velocity
Displacement, Velocity, Acceleration Word Problems

Challenge Quizzes

Displacement, Velocity, Acceleration (Derivatives): Level 2 Challenges
Displacement, Velocity, Acceleration (Derivatives): Level 3 Challenges

Average Velocity

Point $P$ departs from the origin $(0,0)$ at time $t=0$ and travels in a straight line to $(3t, 4t)$ at time $t$ . What is the average speed of $P?$

15 20 5 10

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by Brilliant Staff

A car travels from city $A$ to city $B$ with a speed of $19 \text{ miles/h}$ and back from city $B$ to city $A$ with a speed of $3 \text{ miles/h}.$ What is the average speed of the car (in miles/h) during this round trip?

\displaystyle{ \frac{57}{15} \text{ miles/h}}

\displaystyle{ \frac{57}{11} \text{ miles/h}}

\displaystyle{ 11 \text{ miles/h}}

\displaystyle{ \frac{57}{13} \text{ miles/h}}

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A car leaves point $A$ at $8 \text{am}$ and arrives at point $B$ at $3 \text{pm}$ on the same day. If the car travels a total distance of $623$ miles, then what is its average speed (in miles/hour)?

90 \text{ miles/h}

88 \text{ miles/h}

87 \text{ miles/h}

89 \text{ miles/h}

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The diagram below shows a detour (first $8\text{ m}$ north, then $18\text{ m}$ southeast) from a starting point to an end point. The diagram also shows the shortest distance $12 \text{ m}$ between the starting and end points.

If a person takes the detour and reaches the end point in $23$ seconds, what is the average velocity of the person?

\displaystyle{ \frac{15}{23} \text{ m/s}}

\displaystyle{ \frac{30}{23} \text{ m/s}}

\displaystyle{ \frac{12}{23} \text{ m/s}}

\displaystyle{ \frac{18}{23} \text{ m/s}}

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A runner completes a $126$ meter lap in $13$ seconds. What is average speed of the runner during this lap (in meters/second)?

\displaystyle{ \frac{126}{13} \text{ m/s}}

\displaystyle{ \frac{136}{13} \text{ m/s}}

\displaystyle{ \frac{111}{13} \text{ m/s}}

\displaystyle{ \frac{116}{13} \text{ m/s}}

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by Brilliant Staff