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10.05 Differentiation and kinematics

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
c

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

Easy
1min

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.

Easy
1min

Let $s=10+12t-4.7t^2$s=10+12t4.7t2 be the height of an object in metres at time $t$t in seconds.

Easy
1min

A car starts at rest and has a displacement of $s$s metres in $t$t seconds, where $s=\frac{1}{6}t^3+\frac{1}{4}t^2$s=16t3+14t2.

Easy
2min
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Outcomes

ACMMM094

construct and interpret position-time graphs, with velocity as the slope of the tangent

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