A car, moving along a straight stretch of highway, begins to accelerate at 0.0442 m/s^2. It takes the car 30.8 s to cover 1 km. How fast was the car going when it first began to accelerate?
Answer in units of m/s.
I tried converting 30.8 km/sec to m/s then subtracting 0.0442, but I got -0.0134, and it can't be a negative. I've also tried the answers 30799.558, 13.4, and 0.0134 but my online homework sheet has said they are all wrong. Thanks for the help!
jzee11 that answer wasn't right. I had the exact same numbers as the OP and it said that answer was wrong
To find the initial speed of the car when it first began to accelerate, we can use the equation of motion:
\[v_f = v_i + at\]
where:
- \(v_f\) is the final velocity (speed of the car after 30.8 seconds)
- \(v_i\) is the initial velocity (speed of the car when it first began to accelerate)
- \(a\) is the acceleration (0.0442 m/s^2)
- \(t\) is the time taken (30.8 seconds)
Since the car was initially at rest, the initial velocity \(v_i\) is 0. Plugging these values into the equation, we can solve for \(v_f\):
\[v_f = 0 + (0.0442 \, \text{m/s}^2) \cdot 30.8 \, \text{s}\]
\[v_f = 1.35896 \, \text{m/s}\]
Therefore, the speed of the car when it first began to accelerate was 1.35896 m/s (or approximately 1.36 m/s).
To determine the initial speed of the car when it first began to accelerate, we can use the kinematics equation:
vf = vi + at
Where:
vf is the final velocity
vi is the initial velocity
a is the acceleration
t is the time
In this case, we need to solve for vi.
We are given:
a = 0.0442 m/s^2
t = 30.8 s
First, let's convert the distance traveled from kilometers to meters:
1 km = 1000 m
Next, we need to find the final velocity (vf) using the formula:
vf = (distance traveled) / (time taken)
Given that the distance traveled is 1 km (or 1000 m) and the time taken is 30.8 s:
vf = 1000 m / 30.8 s
Now we can use the kinematics equation to find the initial velocity:
vf = vi + at
Substituting the values we have:
1000 m / 30.8 s = vi + 0.0442 m/s^2 * 30.8 s
Simplifying the equation:
vi + 0.0442 m/s^2 * 30.8 s = 1000 m / 30.8 s
vi + 1.35976 m/s ≈ 32.47 m/s
Now we can solve for vi:
vi ≈ 32.47 m/s - 1.35976 m/s
vi ≈ 31.11024 m/s
Therefore, the car's initial speed when it first began to accelerate was approximately 31.11024 m/s.
Here what i did.
a=0.0442 m/s^2
t1=30.8 s
d=1 km =1000 m.
find the initial velocity (speed)=Vo when car starts accelerating.
From basic equation of acceleration,
a = dv/dt = (V1-Vo)/(t1-t0) ; t0= 0s.
Vo = V1 - a.t1
missing V1=d/t0 = 1000/30.8 = 32.46 m/s.
Then, Vo = 32.46 - (0.0442)(30.8)
=31.1 m/s
tell me answer is correct or not.