NZ Level 7 (NZC) Level 2 (NCEA) Applications of primitive functions

## 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
Approx 4 minutes

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

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.

The velocity of a particle moving in a straight line is given by $v\left(t\right)=6t+15$v(t)=6t+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.

### Outcomes

#### M7-10

Apply differentiation and anti-differentiation techniques to polynomials

#### 91262

Apply calculus methods in solving problems