Calculate initial speed and acceleration given position (on x-axis) and time

In summary, the conversation discusses a problem involving a car driving on a straight road and applying brakes at a constant rate. The goal is to calculate the initial speed and acceleration of the car. The relevant equations for solving the problem are also provided.
  • #1
towng34
1
0

Homework Statement



Help! I have no idea where to begin for this!

You are driving along a straight section of roadway (x-axis). You spot a police officer and apply the brakes, slowing down at a constant rate. Your positions (in meters) at successive time intervals of 0.465 s are tabulated below as function of time. (1) Calculate the initial speed (i.e., the speed at t=0, the time at which the brakes are first applied.). (2) Calculate your acceleration along the x-axis, ax.
x (m) 5.00 21.94 38.25 53.93
t (s) 0.000 0.465 0.930 1.395


Homework Equations




x = x0 + v0t + (1/2)at^2
v = v0 + at
v^2 = v0^2 + 2a(x-x0)

The Attempt at a Solution

 
Physics news on Phys.org
  • #2
Hi towng34, welcome to PF.

If t is the successive interval of time, then

x1 = xo + vo(t) +1/2*a*t^2...(1)

x2 = xo + vo*(2t) +1/2* a*(2t)^2 ...(2)

Find x2 - 2*x1 and solve for a. From that you can find vo.
 

1. What is the formula for calculating initial speed?

The formula for calculating initial speed is initial speed = (final position - initial position)/time. This formula is derived from the equation for average velocity, which is equal to displacement over time.

2. How do I calculate acceleration given position and time?

To calculate acceleration, you need to know the change in velocity and the time taken for that change to occur. The formula for acceleration is acceleration = (final velocity - initial velocity)/time. You can also use the formula acceleration = (change in velocity)/time if the initial velocity is zero.

3. Can I use this formula for non-uniform motion?

No, this formula is only applicable for uniform motion, where the acceleration is constant. For non-uniform motion, you would need to use calculus to find the instantaneous acceleration at a specific point in time.

4. What units should I use for the variables in the formula?

The units for position, velocity, and acceleration are typically measured in meters (m) for distance and meters per second (m/s) for velocity and acceleration. The unit for time is usually measured in seconds (s).

5. Is there a simpler way to calculate initial speed and acceleration?

If you have a graph of position vs. time, you can find the initial speed by calculating the slope of the line at the beginning of the graph. The slope represents the velocity, so you can use this value in the formula for initial speed. Similarly, the slope of the velocity vs. time graph represents the acceleration, so you can use this value in the formula for acceleration.

Similar threads

The final velocity = initial velocity + acceleration x time
    • Introductory Physics Homework Help
Replies
17
Views
1K
Relating acceleration to distance and time
    • Introductory Physics Homework Help
Replies
5
Views
1K
Body Velocity and Position on X-Axis at a Given Moment
    • Introductory Physics Homework Help
Replies
4
Views
932
Help with question on motion: Avoiding a rear-end collision
    • Introductory Physics Homework Help
Replies
6
Views
702
Finding Initial Velocity v0x for Particle with Non-Constant Acceleration
    • Introductory Physics Homework Help
Replies
2
Views
3K
Average speed with constant acceleration over a period of time
    • Introductory Physics Homework Help
Replies
7
Views
1K
Calculating Vx and Vy given V, X, Y
    • Introductory Physics Homework Help
Replies
29
Views
7K
Postion vs time graph without time or initial speed?
    • Introductory Physics Homework Help
Replies
3
Views
1K
Special relativity and acceleration
    • Introductory Physics Homework Help
Replies
3
Views
853
At what time is the velocity perpendicular to the acceleration
    • Introductory Physics Homework Help
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top