NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Displacement, velocity and acceleration (mixed functions)

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/s^{2} after $t$`t` seconds is given by $a=e^{-t}$`a`=`e`−`t`. 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

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