what was the initial velocity of a race car traveling down a long straight track if it accelerates at 5.79m/s^2 and ends up going 163km/h in a time of 3.60 seconds?
Conversion factor:
1 m/s = 3.6 km/h
Δv=(vf-vi)=vi+aΔt
163 km/h = 163/3.6 = 45.28 m/s
45.28=vi+5.79*3.6
vi = 24.4 m/s = 88.0 km/h
To find the initial velocity of the race car, we need to use the formula for acceleration:
v = u + at
Where:
v = final velocity (163 km/h)
u = initial velocity (unknown)
a = acceleration (5.79 m/s^2)
t = time (3.60 seconds)
First, let's convert the final velocity from km/h to m/s:
163 km/h = 163 * (1000 m / 1 km) * (1 h / 3600 s) = 45.3 m/s (rounded to one decimal place)
Now we can substitute the known values into the formula and solve for the unknown initial velocity (u):
45.3 m/s = u + (5.79 m/s^2)(3.60 s)
Multiply the acceleration (5.79 m/s^2) by the time (3.60 s) and subtract it from both sides of the equation:
45.3 m/s - (5.79 m/s^2)(3.60 s) = u
45.3 m/s - 20.9 m/s = u
Simplifying:
u = 24.4 m/s
Therefore, the initial velocity of the race car was 24.4 m/s.