A car with an initial velocity 5m/s initial velocity of 5m/s accelerates uniformly at 3m/s until it reaches 23m/s calculate the time taken and distance travelled during the acceleration
Answers
Answer:
Explanation:
Acceleration
You can calculate the acceleration of an object from its change in velocity and the time taken.
Velocity is not exactly the same as speed. Velocity has a direction as well as a speed. For example, 15 m/s is a speed, but 15 m/s North is a velocity (North is the direction).
Commonly velocities are + (which means forwards) or - (which means backwards).
For example, -15 m/s means moving backwards at 15 metres every second.
The equation
When an object moves in a straight line with a constant acceleration, you can calculate its acceleration if you know how much its velocity changes and how long this takes.
The units for acceleration are commonly written as m/s/s or m/s2. The equation for acceleration can also be represented as:
where:
a is acceleration in m/s/s or m/s2
v is final velocity in m/s
u is initial velocity in m/s
t is time in s
For example, a car accelerates in 5 s from 25 m/s to 3 5m/s. Its velocity changes by 35 - 25 = 10 m/s. Therefore its acceleration is 10 ÷ 5 = 2 m/s2
Deceleration, or negative acceleration, is observed when an object slows down. The units are the same as for acceleration but the number has a negative symbol before it. For example, the car slowed down at -1 m/s2.
Here’s another worked example. This time a car decelerates in 5 s from 35 m/s to 25 m/s. Its velocity changes by 25 - 35 = -10 m/s. Therefore its acceleration is -10 ÷ 5 = -2 m/s2
To Find:-
- Find the distance traveled by the var and time taken.
Solution:-
We can find the time taken by using first equation of motion:-
u= 5m/s ; a = 3m/s^2 ; v = 23m/s ; t = ?
v = u + at
23 = 5 + 3t
23 - 5 = 3t
3t = 18
t = 18/3
t = 6sec
We can find the distance traveled by using first equation of motion:-
u= 5m/s ; a = 3m/s^2 ; v = 23m/s ; t = 6sec ; s = ?
s = ut + 1/2 at^2
s = 5(6) + 1/2 * 3 * 6 * 6
s = 30 + 54
s = 84m