# Thread: Velocity of a car

1. ## Velocity of a car

The Velocity of a car is given by v(t)=120(1-0.85^t)

How can i calculate the average and instant acceleration of the car in the first 5 seconds/

2. ## Re: Velocity of a car

Originally Posted by waleedrabbani
The Velocity of a car is given by v(t)=120(1-0.85^t)

How can i calculate the average and instant acceleration of the car in the first 5 seconds/
average acceleration from $t = 0$ to $t = 5$ ...

$\bar{a} = \frac{v(5)-v(0)}{5-0}$

understand that the instantaneous acceleration calculation requires calculus.

$a(t) = v'(t)$

What do you know about derivatives of exponential functions?

3. ## Re: Velocity of a car

my teacher never taught us derivities instead we use something like (f(X)+(X.0001))/.0001

4. ## Re: Velocity of a car

Originally Posted by waleedrabbani
my teacher never taught us derivities instead we use something like (f(X)+(X.0001))/.0001
ok, then ... you're making an estimate of the instantaneous rate of change of velocity. get out your calculator and do it.

$a(5) \approx \frac{v(5.0001) - v(5)}{5.0001 - 5}$