Differentiation

New Zealand

Level 7 - NCEA Level 2

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`)=6`t`2.

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`)=3`t`3−4`t`2.

Easy

1min

The position (in metres) of an object along a straight line after $t$`t` seconds is modelled by $x\left(t\right)=3t^2+5t+2$`x`(`t`)=3`t`2+5`t`+2.

We want to find the velocity of the object after $4$4 seconds.

Easy

1min

The position (in metres) of an object along a straight line after $t$`t` seconds is modelled by $x\left(t\right)=18\sqrt{t}$`x`(`t`)=18√`t`.

Easy

2min

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