12.10 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 $t\ge0$t≥0.
The object is initially at the origin. That is, $x\left(0\right)=0$x(0)=0.
State the displacement $x\left(t\right)$x(t) of the particle at time $t$t. Use $c$c as the constant of integration.
Solve for the time $t$t at which the particle is $100$100 m to the right of the origin.
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 $t\ge0$t≥0
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 $t\ge0$t≥0.
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.
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)=6√t.
The object is initially $7$7 metres to the right of the origin.