If a car has an initial velocity of 103m/s and accelerates at 1m/s for 3 seconds, what will its final velocity be? Can you please show me how to work this question out with math answers and explain it to me. Thank you.
We start counting when it's moving 103m/s. (And incidentally, that's pretty fast for a car. Formula 1, maybe?)
Each second after that, it moves 1m/s faster than it was before.
So if we call time by seconds, as we often do in these things, we call the start, after zero seconds, t0.
t0 = 103 m/s
After one second, it's moving 1m/s faster:
t1 = 104 m/s
The next second, 1m/s faster again...
t2 = 105 m/s
and finally...
t3 = 106 m/s
In general, after n seconds, it's moving at (103 + n) m/s.
It's actually accelerating at 1 m/s^2, or "one meter per second per second" since it gets 1 meter per second faster every second.
I used a shorthand that was wrong in this question, and it might confuse you.
When I say
t0 = 103 m/s
what I should have said, to be clear, was
speed at t0 = 103 m/s
and so on.
To find the final velocity of the car, we can use the equation of motion:
final velocity = initial velocity + (acceleration × time)
In this case, the initial velocity is 103 m/s, the acceleration is 1 m/s², and the time is 3 seconds.
Substituting these values into the equation, we get:
final velocity = 103 m/s + (1 m/s² × 3 s)
Multiplying the acceleration (1 m/s²) by the time (3 s), we get:
final velocity = 103 m/s + 3 m/s
Adding the two velocities together, we get:
final velocity = 106 m/s
Therefore, the final velocity of the car will be 106 m/s.
In summary, the process to find the final velocity involves using the equation of motion and substituting the given values of initial velocity, acceleration, and time. By performing the necessary calculations, we find the final velocity of the car.