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New Zealand
Level 8 - NCEA Level 3

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.


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.


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

Approx 9 minutes
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A particle accelerates according to the equation


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.



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


Apply differentiation methods in solving problems

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