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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 $v\left(t\right)=12t$v(t)=12t, 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 $54$54 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 $v\left(t\right)=6t+10$v(t)=6t+10, where $t\ge0$t0

Easy
3min

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 $v\left(t\right)=12t^2+30t+9$v(t)=12t2+30t+9, where $t\ge0$t0.

The object starts its movement at $6$6 metres to the left of the origin. That is, $s\left(0\right)=-6$s(0)=6.

Easy
2min

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 $v\left(t\right)=12\sqrt{t}$v(t)=12t.

The object is initially $5$5 metres to the right of the origin.

Easy
4min
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Outcomes

ACMMM123

determine displacement given velocity in linear motion problems

ACMMM135

determine positions given acceleration and initial values of position and velocity

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