Differentiation

New Zealand

Level 7 - NCEA Level 2

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`)=12`t`, where $t\ge0$`t`≥0.

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`)=6`t`+10, where $t\ge0$`t`≥0

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`)=12`t`2+30`t`+9, where $t\ge0$`t`≥0.

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 of a particle moving in a straight line is given by $v\left(t\right)=6t+15$`v`(`t`)=6`t`+15, where $v$`v` is the velocity in metres per second and $t$`t` is the time in seconds.

The displacement after $2$2 seconds is $45$45 metres to the right of the origin.

Easy

4min

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