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Speed / Velocity Time Graphs

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Question

Starting from rest at $t = 0,$ a car moves in a straight line with an acceleration given by the accompanying graph. The speed of the car at $t = 3 s$ is :

m s^{- 1}

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m s^{- 1}

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6.0

{m s}^{- 1}

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10.5

{m s}^{- 1}

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Solution

The correct option is D 10.5 ${m s}^{- 1}$
$\frac{d v}{d t} = 0$
$\Rightarrow \int d v = \int a d t$
$v - v_{0} =$ Area of $a - t$ graph
$\Rightarrow v - 0 = \frac{1}{2} \times 3 \times (5 + 2)$
$\Rightarrow v = 10.5 m / s$

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Starting from rest at t=0, a car moves in a straight line with an acceleration given by the accompanying graph. The speed of the car at t=3s is :

The correct option is D 10.5ms−1dvdt=0⇒∫dv=∫adtv−v0= Area of a−t graph⇒v−0=12×3×(5+2)⇒v=10.5m/s

Starting from rest at $t = 0,$ a car moves in a straight line with an acceleration given by the accompanying graph. The speed of the car at $t = 3 s$ is :

The correct option is D 10.5 ${m s}^{- 1}$
$\frac{d v}{d t} = 0$
$\Rightarrow \int d v = \int a d t$
$v - v_{0} =$ Area of $a - t$ graph
$\Rightarrow v - 0 = \frac{1}{2} \times 3 \times (5 + 2)$
$\Rightarrow v = 10.5 m / s$