Calculating Acceleration and Displacement in 1D Motion

In summary, to solve the given problem, we use the formula a=(v-u)/t to find the acceleration and s=((u+v)*t)/2 to find the displacement. In this case, the acceleration is 3 m/(s^2) and the displacement is 37.5 m.
  • #1
SarahV
1
0
:confused: :confused: Help! I need to know how to work this problem! A motorcyclist moving with an initial velocity of 8.0 m/s undergoes a constant acceleration for 3.0s, at which time his velocity is 17.0 m/s. What is the acceleration, and how far does he travel in the 3.0 s interval?
 
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  • #2
aceeleration=change in velocity/change in time so:
17-8/3=a
d=at
so d=a * 3 seconds
 
  • #3
SarahV said:
:confused: :confused: Help! I need to know how to work this problem! A motorcyclist moving with an initial velocity of 8.0 m/s undergoes a constant acceleration for 3.0s, at which time his velocity is 17.0 m/s. What is the acceleration, and how far does he travel in the 3.0 s interval?

Actually, d=at is incorrect.
The correct formula is [tex] v^2 - u^2 = 2as [/tex]. u is the initial velocity, in this case 8 m/s. We know [tex] a = 3 m/s^2 [/tex], therefore [tex] 17^2 - 8^2 = 2(3)s [/tex] and so [tex] s = (17^2 - 8^2)/6 [/tex] which turns out to be 37.5 m.
 
  • #4
8+3a=17
a=3m/s^2
8*3+0.5*3*3^2=24+13.5=37.5m
 
  • #5
Let me summarize the solution.

a=acceleration u=initial velocity v=final velocity
s=displacement t=time taken

a=(v-u)/t
a=(17.0-8.0)/3.0
a=3 m/(s^2)

s=((u+v)*t)/2
s=((8.0+17.0)*3.0)/2
s=37.5 m

Therefore, the acceleration is 3 m/(s^2) to his original direction and
the displacement he traveled is 37.5 m to his original direction.
 
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1. What is motion in 1 dimension?

Motion in 1 dimension refers to the movement of an object along a single straight line. This can also be referred to as linear motion.

2. What are the key variables that describe motion in 1 dimension?

The key variables that describe motion in 1 dimension are displacement, velocity, and acceleration. Displacement refers to the change in position of an object, velocity is the rate of change of displacement, and acceleration is the rate of change of velocity.

3. How is motion in 1 dimension represented graphically?

Motion in 1 dimension is often represented graphically using a position vs. time graph. This graph shows the displacement of an object over a period of time, with the slope representing the object's velocity and the curvature representing its acceleration.

4. What is the difference between speed and velocity?

Speed and velocity are often used interchangeably, but they have different meanings in the context of motion in 1 dimension. Speed refers to the rate at which an object is moving, while velocity refers to the rate and direction of an object's motion.

5. How is acceleration calculated for an object in 1 dimension?

Acceleration can be calculated for an object in 1 dimension using the formula a = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time interval. This formula can also be rearranged to solve for final or initial velocity or time, depending on the given information.

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