A point Q moves in a straight line with velocity v ms−1 given by v ( t ) = e − t − 8 t 2 e − 2 t at timet seconds, wheret≥ 0.

Question

HLPaper 2

A point Q moves in a straight line with velocity $v$ ms⁻¹ given by $v\left( t \right) = {{\text{e}}^{ - t}} - 8{t^2}{{\text{e}}^{ - 2t}}$ at timet seconds, wheret≥ 0.

Find the value of the acceleration of Q at time t₁.

Verified

Solution

$a\left( {{t_1}} \right) = - 2.28$ (ms⁻²) A1

[1 mark]

Determine the first time t₁ at which Q has zero velocity.

Verified

Solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

attempt to solve $v\left( t \right) = 0$ fort or equivalent (M1)

t₁= 0.441(s) A1

[2 marks]

Find an expression for the acceleration of Q at time t.

Verified

Solution

$a\left( t \right) = \frac{{{\text{d}}v}}{{{\text{d}}t}} = - {{\text{e}}^{ - t}} - 16t{{\text{e}}^{ - 2t}} + 16{t^2}{{\text{e}}^{ - 2t}}$ M1A1

Note: Award M1 for attempting to differentiate using the product rule.

[2 marks]

Still stuck?

Get step-by-step solutions with Jojo AI

Free

Want more practice questions for Mathematics Applications & Interpretation (Math AI)?

A point Q moves in a straight line with velocity v ms−1 given by v ( t ) = e − t − 8 t 2 e − 2 t at timet seconds, wheret≥ 0.

Related topics