NZ Level 8 (NZC) Level 3 (NCEA) [In development] Displacement, velocity and acceleration (mixed functions)

## Interactive practice questions

A particle $P$P starts off from a fixed point $O$O, with an initial velocity of $2$2 m/s. Its acceleration $a$a m/s2 after $t$t seconds is given by $a=e^{-t}$a=et. The velocity of the particle is $v$v.

a

Find $v\left(4\right)$v(4), the velocity of $P$P after $4$4 seconds. Give your answer correct to two decimal places, and use $C$C as the constant of integration.

b

Find the displacement, $x$x, of the particle $P$P after $4$4 seconds, correct to the nearest hundredth of a metre.

Easy
Approx 9 minutes

A particle accelerates according to the equation

$a=-e^{4t}$a=e4t

where $a$a is measured in cm/s².

A particle moves in a straight line so that after $t$t seconds ($t\ge0$t0) its velocity $v$v is given by $v=\frac{3}{1+t}-t+1$v=31+tt+1 m/s. The displacement of the particle from the origin is given by $x$x metres.

The acceleration of a particle is given by $a\left(t\right)=2e^{3t}$a(t)=2e3t m/s², and its velocity is $10$10 m/s initially.

### Outcomes

#### M8-11

Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods

#### 91578

Apply differentiation methods in solving problems