Question

3. If a car can go from 0 to 100 km/hr in 8.0 seconds, what would be its final speed after 5.0
seconds if its starting speed were 80 km/hr?
please show work

Answer 1

The final speed of the car after 5.0 seconds, if its starting speed were 80 km/hr is 142.45 km/hr

Given the data in the question;

Initially, the car starts from 0 to 100 km/hr in 8 seconds

That is to say that;

Initial velocity; $u = 0m/s$

Final velocity; $v = 100km/h = 27.7778 m/s$ {convert to meter per seconds}

Time; $t = 8s$

First we find the acceleration "a" using the first equation of motion which states that;

$v = u + at$

Make "a" the subject of the formula

$a = \frac{v-u}{t}$

Next, we input our given  values

$a = \frac{27.7778m/s\ -\ 0m/s}{8s}$

$a = 3.47 m/s^2$

]Now, what would be its final speed after 5.0 seconds if its starting speed were 80 km/hr.

That is; Initial speed; $u_2 = 80 km/hr = 22.22m/s$

Time; $t_2 = 5s$

We already know that acceleration; $a = 3.47 m/s^2$

Final speed; v₂ = ?

To find the final velocity, we still make use of the first equation equation of motion; which states that;

$v = u + at$

Meaning, $v_2 = u_2 + at_2$

Now, since we are looking for the final velocity "v", we simply input our values into the equation.

$v_2= 22.22 m/s\ + ( 3.47m/s^2 \ * \ 5s )$

$v_2 = 39.57 m/s$

We convert back to kilometer per hour

$v_2 = 142.45 km/hr$

Therefore, The final speed of the car after 5.0 seconds, if its starting speed were 80 km/hr is 142.45 km/hr

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