a) A car accelerates uniformly from rest to a speed of 97.9 mi/h in 6.93 s.Find the constant acceleration of the car.Answer in units of m/s^2.
b)Find the distance that the car travels during this time.Answer in units of m.
How do you do this?
convert 97.9mi/hr to m/s
Put this in your google search window:
97.9miles/hr in m/s=
Then, acceleration=velocity/time
distance=avg speed*time
= v/2 * time
To find the constant acceleration of the car, you can use the kinematic equation:
\(v = u + at\)
where:
- \(v\) is the final velocity (97.9 mi/h)
- \(u\) is the initial velocity (0 mi/h, since the car starts from rest)
- \(a\) is the acceleration (what we want to find)
- \(t\) is the time taken (6.93 s)
1. Convert the given velocities to meters per second (m/s):
- \(97.9 \, \text{mi/h} \rightarrow\) first convert miles to meters by multiplying by 1609.34 (1 mile = 1609.34 m)
- Now convert hours to seconds by multiplying by 3600 (1 hour = 3600 s)
- So, \(97.9 \, \text{mi/h} = 97.9 \times 1609.34/3600 \, \text{m/s}\)
2. Substitute the known values into the equation and solve for \(a\):
\(v = u + at\) becomes
\(97.9 \times 1609.34/3600 = 0 + a \times 6.93\)
Rearrange the equation to solve for \(a\):
\(a = (97.9 \times 1609.34/3600) / 6.93\)
Calculate the value of \(a\) using a calculator. The result will be in meters per second squared (m/s^2).
To find the distance traveled during this time, you can use another kinematic equation:
\(s = ut + \frac{1}{2}at^2\)
where:
- \(s\) is the distance traveled (what we want to find)
3. Substitute the known values into the equation and solve for \(s\):
\(s = 0 \times 6.93 + \frac{1}{2} \times a \times (6.93)^2\)
Calculate the value of \(s\) using a calculator. The result will be in meters (m).