Question

a car is moving 8.80 m/s when it begins to accelerate at 2.45 m/s^2. how much time does it take to trav 138m. please help me (': ​

Answer 1

7.6 s

Step-by-step explanation:

Considering kinematics formula for final velocity as

`v^(2)=u^(2)+2as`

Where v and u are final and initial velocities, a is acceleration and s is distance moved.

Making v the subject then

`v=\sqrt{u^(2)+2as}`

Substituting 8.8 m/s for u, 138 m for s and 2.45 m/s2 for a then

`v=\sqrt{8.8^(2)+2*2.45*138}\\v=27.45 m/s`

Also, v=u+at and making t the subject of the formula

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

Substituting 27.45 m/s for v, 8.8 m/s for u and 2.45 m/s for a then

`t=\frac {27.45-8.8}{2.45}=7.6122448979591\approx 7.6s`

Therefore, it needs 7.6 seconds to travel