Acceleration - free fall
How long will it take for a car to reach speed of 180 km/h with an acceleration of 10 m/s2?
Final Answer:
Showing 1 comment:
Dr. Math
To determine how long it will take for a car to reach a speed of 180 km/h with an acceleration of 10 m/s², we will use the kinematic equation for uniformly accelerated motion:
where:
- v = final velocity (in m/s),
- u = initial velocity (in m/s),
- a = acceleration (in m/s²),
- t = time (in seconds).
The final velocity is given in km/h, but we need it in m/s for consistency with the acceleration units. Convert 180 km/h to m/s:
The car starts from rest, so the initial velocity is:
The kinematic equation is:
Solve for t :
Substitute v = 50 m/s , u = 0 m/s , and a = 10 m/s² :
The car will take:
v = u + at
where:
- v = final velocity (in m/s),
- u = initial velocity (in m/s),
- a = acceleration (in m/s²),
- t = time (in seconds).
Step 1:
Convert Final Velocity to m/sThe final velocity is given in km/h, but we need it in m/s for consistency with the acceleration units. Convert 180 km/h to m/s:
v = 180 × 10003600 = 50 m/s.
Step 2:
Identify Initial VelocityThe car starts from rest, so the initial velocity is:
u = 0 m/s.
Step 3:
Rearrange the Kinematic EquationThe kinematic equation is:
v = u + at.
Solve for t :
t = v - ua.
Step 4:
Substitute Values and Solve for tSubstitute v = 50 m/s , u = 0 m/s , and a = 10 m/s² :
t = 50 - 010 = 5 seconds.
Final Answer:
The car will take:
5 seconds
Tips for related online calculators
Do you want to convert velocity (speed) units?
Do you want to convert time units like minutes to seconds?
Do you want to convert time units like minutes to seconds?
You need to know the following knowledge to solve this word math problem:
Units of physical quantitiesthemes, topicsGrade of the word problem
Related math problems and questions:
- Car acceleration distance
How far must a car travel to reach a speed of 72 km per hour if it starts from rest in a uniformly accelerated motion with an acceleration of 0.2 meters per second²? - Car acceleration runway
The car reaches a steady acceleration in 24 seconds from a standstill speed of 100 km/h. What runways will he reach on departure? - The satellite
The satellite orbiting the Earth at an altitude of 800 km has a speed of 7.46 km/s. How long would it have to move from the start to the orbit to reach this speed if it evenly accelerated its motion in a straight line? What is the acceleration of satellit - Car braking acceleration The car stopped at an initial speed of 90 km/h on a track of 62.5 m. What was its acceleration, and how long did it take to brake the car?
- Braking acceleration
At the start of braking, the car had a speed of 72 km h at -1. It stopped on a track of 50 m. What was the acceleration, and how long did the braking last? - Vehicle speed
An accompanying vehicle set off behind the car with an oversized load moving at a speed of 16 km/h in 2.5 hours, which must reach it in 45 minutes. What speed does he have to go? - Speed of car
The car went to a city that was 240 km away. If his speed increased by 8 km/h, it would reach the finish one hour earlier. Determine its original speed.
