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5.04 Kinematics and integration

Interactive practice questions

The velocity $v\left(t\right)$v(t) (in metres per second) of an object travelling horizontally along a straight line after $t$t seconds is modelled by $v\left(t\right)=8t$v(t)=8t, where $t\ge0$t0.

The object is initially at the origin. That is, $x\left(0\right)=0$x(0)=0.

a

State the displacement $x\left(t\right)$x(t) of the particle at time $t$t. Use $c$c as the constant of integration.

b

Solve for the time $t$t at which the particle is $100$100 m to the right of the origin.

Easy
4min

The velocity $v$v (in metres) of an object travelling horizontally along a straight line after $t$t seconds is modelled by $v\left(t\right)=6t+5$v(t)=6t+5, where $t\ge0$t0

Easy
5min

The velocity $v\left(t\right)$v(t) (in metres) of an object travelling horizontally along a straight line after $t$t seconds is modelled by $v\left(t\right)=15t^2+24t+4$v(t)=15t2+24t+4, where $t\ge0$t0.

The object starts its movement at $5$5 metres to the left of the origin. That is, $s\left(0\right)=-5$s(0)=5.

Easy
5min

The velocity $v\left(t\right)$v(t) (in metres/s) of an object along a straight line after $t$t seconds is modelled by $v\left(t\right)=6\sqrt{t}$v(t)=6t.

The object is initially $7$7 metres to the right of the origin.

Easy
6min
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Outcomes

3.2.21

determine displacement given velocity in linear motion problems

3.2.22

determine positions given linear acceleration and initial values of position and velocity

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