Differentiation

NZ Level 7 (NZC) Level 2 (NCEA)

Applications of primitive functions

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

Approx 4 minutes

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