New Zealand
Level 7 - NCEA Level 2

# Speed, displacement and velocity

## Interactive practice questions

The position (in metres) of an object along a straight line after $t$t seconds is modelled by $x\left(t\right)=6t^2$x(t)=6t2.

a

State the velocity $v\left(t\right)$v(t) of the particle at time $t$t.

b

Which of the following represent the velocity of the particle after $4$4 seconds? Select all that apply.

$x'\left(4\right)$x(4)

A

$v'\left(4\right)$v(4)

B

$x\left(4\right)$x(4)

C

$v\left(4\right)$v(4)

D

$x'\left(4\right)$x(4)

A

$v'\left(4\right)$v(4)

B

$x\left(4\right)$x(4)

C

$v\left(4\right)$v(4)

D
c

Hence find the velocity of the particle after $4$4 seconds.

Easy
Approx 2 minutes

The position (in metres) of an object along a straight line after $t$t seconds is modelled by $x\left(t\right)=3t^3-4t^2$x(t)=3t34t2.

The position (in metres) of an object along a straight line after $t$t seconds is modelled by $x\left(t\right)=3t^2+5t+2$x(t)=3t2+5t+2.

We want to find the velocity of the object after $4$4 seconds.

The position (in metres) of an object along a straight line after $t$t seconds is modelled by $x\left(t\right)=18\sqrt{t}$x(t)=18t.

### Outcomes

#### M7-10

Apply differentiation and anti-differentiation techniques to polynomials

#### 91262

Apply calculus methods in solving problems