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Calculus

Displacement, Velocity, Acceleration

Concept Quizzes

Finding Displacement given Velocity
Finding Velocity given Acceleration
Uniform Acceleration

Challenge Quizzes

Displacement, Velocity, Acceleration (Integrals): Level 2-3 Challenges

Finding Displacement given Velocity

A particle moves along the $x$ -axis with velocity $v(t)=30t^2-90t+60$ at time $t$ . Find the total distance covered between time $t=0$ and time $t=5.$

420 425 430 435

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The above is the velocity-time graph of a runner. How far does this runner travel for $16$ seconds?

The figure’s vertical scaling is set by $v_{s} = 8.0 \text{ m/s.}$

50 m 200 m 150 m 100 m

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A train starts from station $A$ and arrives at station $B$ in $6$ minutes. If the velocity of the train in $\text{m/min}$ is $v(t) = 24t^2(6-t),$ what is the distance between the two stations $A$ and $B?$

7776

2592

10368

5184

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by Brilliant Staff

Sam throws a ball straight upward at a speed of $30 \text{ m/s}$ from the edge of a cliff $19 \text{ m}$ high, as shown in the above diagram. If the the velocity of the ball $t$ seconds after the ball leaves his hand is $v=30-10t$ (in $\text{m/s}$ ), what is the distance of the ball from the ground $3$ seconds after the ball leaves his hand?

62 \text{ m}

67 \text{ m}

65 \text{ m}

64 \text{ m}

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Two points $P$ and $Q$ start at the origin and move from the origin at the same time along the $x$ -axis. At time $t>0$ , $P$ and $Q$ have velocities of $\sin (\pi t)$ and $2\sin (2\pi t)$ , respectively. If $P$ and $Q$ first meet again after $\frac{m}{n}$ seconds, where $m$ and $n$ are positive co-prime integers, what is the value of $m+n$ ?

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by Brilliant Staff