How Do You Calculate Velocity from a Position-Time Equation?

• chound
In summary, the conversation involves a discussion about finding the velocity of an object moving along the x-axis. The position of the object is given by the equation x=a+b(t*t), where a=8.5m, b=2.5m/(s*s), and t is time. The participants suggest using differential calculus to find the velocity at t=2s. They also mention differentiating the equation and solving for v(t).
chound
The position of an object moving along x-axis is given by x=a+b(t*t) where a =8.5m, b=2.5m/(s*s) and t is time. What is the velocity at t=2s? I think differential calculus should be used

If that x equation is x = a+bt^2, then just differentiate wrt to time to get velocity.

Yupp, just get dx/dt and then make t = 2.

Is it this:
dx/dt = d(a+bt^2)/dt
After this what should I do?

Do you know how to differentiate?

If $y = a + bx^2$, what is dy/dx?

You have $x = a + bt^2$, and you know v=dx/dt, so what is v(t)?

1. What is velocity and how is it different from speed?

Velocity refers to the rate of change of an object's position with respect to time. It is a vector quantity that includes both magnitude and direction. Speed, on the other hand, is a scalar quantity that only measures the magnitude of an object's motion. In other words, velocity takes into account the direction of an object's movement while speed does not.

2. How do I calculate velocity?

Velocity can be calculated by dividing the change in position (displacement) by the change in time. This can be represented by the equation: velocity = displacement / time. It is important to note that velocity is measured in units of distance per unit time, such as meters per second (m/s) or kilometers per hour (km/h).

3. What is the difference between average and instantaneous velocity?

Average velocity is calculated by dividing the total displacement by the total time, while instantaneous velocity refers to the velocity of an object at a specific moment in time. Average velocity gives an overall picture of an object's motion, while instantaneous velocity gives a more precise measurement at a specific point in time.

4. How does acceleration affect velocity?

Acceleration is the rate of change of an object's velocity with respect to time. If an object's acceleration is constant, it will cause a change in the object's velocity over time. If an object's acceleration is positive, it will increase its velocity, while a negative acceleration will decrease its velocity.

5. Can velocity be negative?

Yes, velocity can be negative. This indicates that the object is moving in the opposite direction of the chosen point of reference. For example, if a car is traveling westward, its velocity would be negative if the chosen point of reference is eastward. However, the magnitude of the velocity (speed) will always be positive.

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