## Statement

difficulty

A meteorite moves through space with a velocity v⃗(t) = (1+4·t) i⃗+t2 j⃗ m. Calculate

a) Its average acceleration between the times t1=2 s and t2= 4 s.
b) Its acceleration at t3= 6 s.

## Solution

Question a)

Data

v⃗(t) = (1+4·t) i⃗+t2 j⃗ m

t1=2 s y t2=4 s

Resolution

To calculate the average acceleration we must use the following equation:

${\stackrel{\to }{a}}_{a}=\frac{{\stackrel{\to }{v}}_{2}-{\stackrel{\to }{v}}_{1}}{{t}_{2}-{t}_{1}}=\frac{∆\stackrel{\to }{v}}{∆t}$

We know t1 and t2. Now we need to calculate the velocity at the instant t1 (v⃗1) and at the time t2 (v⃗2). So, just substitute in the equation of velocity that was provided in the statement of the exercise:

For t1=2 s

For t2=4 s

Substituting in the first equation:

Question b)

Data

v⃗(t) = (1+4·t) i⃗+t2 j⃗ m
t3= 6 s

Resolution

To calculate the acceleration at time t3 we must first calculate the average acceleration:

Taking the derivative of velocity with respect to time we get that:

and substituting the value for t3= 6 s.

## Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Formulas
Related sections
${\stackrel{\to }{a}}_{a}=\frac{{\stackrel{\to }{v}}_{2}-{\stackrel{\to }{v}}_{1}}{{t}_{2}-{t}_{1}}=\frac{∆\stackrel{\to }{v}}{∆t}$