After $t$t seconds, the position of a particle is $x$x metres, its velocity is $v$v m/s and its acceleration is $a$a m/s^{2}.

If $v^2=4-x^2$v2=4−x2, express $a$a in terms of $x$x.

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After $t$t seconds, the position of a particle from a fixed point is $x$x metres, its velocity is $v$v m/s and its acceleration is $a$a m/s^{2}.

If $v=x+3$v=x+3, express $a$a in terms of $x$x.

The velocity $v$v of a particle at position $x$x can be modelled using the following relationship $v^2=4\left(9-x^2\right)$v2=4(9−x2).

Express its acceleration $a$a as a function of $x$x.

After $t$t seconds, the position of a particle is $x$x metres, its velocity is $v$v m/s and its acceleration is $a$a m/s^{2}.

If $\frac{dx}{dt}=e^{4x}$dxdt=e4x, express $a$a in terms of $x$x.

Outcomes

M8-11

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