A car, moving along a straight stretch of highway,

begins to accelerate at 0.024 m/s
2
. It
takes the car 61.8 s to cover 1 km.
How fast was the car going when it first
began to accelerate?

average velocity=1000m/61.8 sec=16.18m/s= 1/2 (vf+vi) or

vf+vi=32.36m/s
Now, vf=vi+at
vf-vi=.024*61.8=1.48

so now you have two equations, subtract the second from the first.
2Vi=32.36-1.48 and solve.

To find the initial speed of the car when it first began to accelerate, we need to use the formula of accelerated motion:

v = u + at

Where:
v = final velocity (unknown)
u = initial velocity (unknown)
a = acceleration (0.024 m/s^2)
t = time (61.8 s)

Since the car started from rest (initial velocity is zero), we can simplify the equation to:

v = 0 + (0.024 m/s^2) * (61.8 s)

Now, we can calculate the final velocity:

v = 0.024 m/s^2 * 61.8 s

v = 1.4832 m/s

However, the answer is required in km/h, so we need to convert it:

1 m/s = 3.6 km/h

v = 1.4832 m/s * 3.6 km/h/m/s

v ≈ 5.34 km/h

Therefore, the car was going approximately 5.34 km/h when it first began to accelerate.

To find out how fast the car was going when it first began to accelerate, we can use the following equation:

v = u + at

Where:
v = final velocity
u = initial velocity
a = acceleration
t = time

We have the following information:
a = 0.024 m/s^2
t = 61.8 s

We need to convert 1 km to meters:
1 km = 1000 meters

Now, let's calculate the final velocity.

Substituting the values into the equation, we have:

v = u + at

v = u + (0.024 m/s^2)(61.8 s)

v = u + 1.4832 m/s

Now, we know that it takes the car 61.8 s to cover 1 km, which is 1000 meters.

So, we can write the equation as:

1000 meters = u(61.8 s) + (1/2)(0.024 m/s^2)(61.8 s)^2

Let's simplify the equation:

1000 meters = 61.8u + 0.024(1/2)(61.8 s)^2

1000 meters = 61.8u + 0.012(61.8 s)^2

Now, solve for u:

61.8u = 1000 meters - 0.012(61.8 s)^2

61.8u = 1000 meters - 0.012(61.8)^2 s^2

61.8u = 1000 meters - 0.012(61.8)^2 s^2

61.8u = 1000 meters - 46.582s^2

Now, divide both sides by 61.8:

u = (1000 meters - 46.582s^2) / 61.8

Substituting the values:

u = (1000 meters - 46.582(61.8 s)^2) / 61.8

Solving this equation will give us the initial velocity when the car first began to accelerate.