Solving Kinematic Equations: Acceleration from 100m in 9.77s

In summary, the person ran 100 m in 9.77 seconds with a maximum speed of 10.23 m/s reached in 3 seconds. The acceleration during the first 3 seconds can be found by using the equation (final velocity - initial velocity)/time, resulting in an acceleration of 3.41 m/s^2. To find the displacement and velocity at 3 seconds and 9.77 seconds, equations containing the acceleration variable can be used. However, it is not possible to solve the equations with two missing variables without additional information.
  • #1
A person runs 100 m in 9.77 s. Maximum speed was reached in 3 s, then maintained for the rest of the time. What was the acceleration during the first 3 seconds?

I know that I can find the average velocity, which is 100 m/9.77 s, and i know that initial velocity is 0 m/s. I don't know how to find the acceleration because I don't know what the velocity is. Could anyone guide me through the methodology of this problem? I don't want the numerical answer.
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  • #2
it can be like this.
initial velocity=0
velocity at the end of 3 sec is100/9.77m/s i.e. 10.23m/s
now acc. = (final vel. - initial vel.)/time=(10.23-0)/3=3.41m/sec.sq
so,acc. after 3 sec is 3.41m/sec.sq
  • #3
The system is telling me that that is incorrect.
  • #4
Find the displacement and velocity at 3 seconds. Find the displacement and velocity at 9.77 seconds.
  • #5
How do I find displacement and velocity if I don't know acceleration?
  • #6
I meant, find equations for them (the equations will contain "a").
  • #7
I don't understand how I can solve the equations with two missing variables.

1. How do you calculate acceleration from a given distance and time?

Acceleration can be calculated using the equation a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time. In this case, the given distance of 100m can be used as the displacement (vf - vi) in the equation.

2. Why is acceleration important in kinematics?

Acceleration is important in kinematics because it represents the rate of change of velocity. It provides information about how quickly an object is speeding up or slowing down, and is necessary for accurately describing an object's motion.

3. What is the difference between acceleration and velocity?

Velocity is a vector quantity that describes the speed and direction of an object's motion, while acceleration is a vector quantity that describes the rate of change of an object's velocity. In other words, velocity tells us how fast and in which direction an object is moving, while acceleration tells us how much an object's velocity is changing over time.

4. Can acceleration be negative?

Yes, acceleration can be negative. A negative acceleration, also known as deceleration, means that an object is slowing down. This can happen when the initial velocity is greater than the final velocity, or when the direction of the acceleration is opposite to the direction of the velocity.

5. How can kinematic equations be applied in real-world situations?

Kinematic equations can be applied in various real-world situations, such as calculating the acceleration of a roller coaster, determining the speed of a car in a car chase, or predicting the trajectory of a basketball shot. These equations allow us to analyze and understand the motion of objects in our everyday lives.

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