A car enters the freeway with a speed of 7.2 m/s south and accelerates uniformly for 4.2 km in 4.0 min. How fast (in m/s) is the car moving after this time?
I only need the formula.
My teacher gave us a list but did not tell the class which equation is for which.
Help please.
x = Xi + Vi t + (1/2) a t^2
4200 = 0 + 7.2 t + (1/2) a t^2
but t = 4 * 60 = 240 seconds
so
4200 = 7.2(240) + .5 a (240)^2
solve for a
then
v = Vi + a t
v = 7.2 + a (240)
Thank you so much! You didn't have to solve it for me, I only needed the formula, but thanks a lot!^^
To find the speed of the car after a given time, we can use the formula for uniform acceleration:
v = u + at
where:
v = final velocity (speed) of the car
u = initial velocity (speed) of the car
a = acceleration of the car
t = time taken
In this problem, the car enters the freeway with an initial velocity of 7.2 m/s (south) and accelerates uniformly for 4.0 min (or 4.0 x 60 = 240 seconds). We need to convert the 4.2 km to meters, which is 4200 meters.
First, let's assign the known values:
u = 7.2 m/s
a = ?
t = 240 s
We need to find the acceleration (a) in order to use the formula. To do that, we can use the equation for uniform acceleration:
a = (v - u) / t
In this case, we want to find the final velocity (v), so we rearrange the formula:
v = u + at
Substituting the known values:
v = 7.2 m/s + a * 240 s
Now, we also know that the car accelerates for a distance of 4200 meters. The formula relating acceleration (a), initial velocity (u), final velocity (v), and distance (d) is given by:
v^2 = u^2 + 2ad
We can rearrange this formula to find the acceleration (a):
a = (v^2 - u^2) / (2d)
Substituting the known values:
a = (v^2 - (7.2 m/s)^2) / (2 * 4200 m)
Now, we have two equations with two unknowns (v and a). We can solve these equations simultaneously to find the final velocity (v) after 4.0 minutes.
Please note that without the specific values for acceleration, these equations will only give you the general formulas to solve similar problems.