Solving Differentiation Help: Find Time When Acceleration = 0

In summary, the problem is asking to find the time when the acceleration of a particle is first zero. By differentiating the given velocity equation, we get 5cos(1/2t) and setting it equal to zero, we solve for t = 1/2 arc cos 0, which simplifies to t = pi.
  • #1
RoryP
75
0
Differentiation Help!

Homework Statement


A particle is moving along a straight line so that, at time t seconds after leaving a fixed point O, its velocity vms-1 is given by v=10sin(1/2 t).
Find the time when the acceleration, given by dv/dt, is first zero.

Homework Equations


sinx differentiates to cosx

The Attempt at a Solution


Ok i know they are asking me to find the time where there is a stationary point so therefore the gradient or dv/dt = 0.
From differentiating 10sin(1/2 t) i got 5cos(1/2 t). so therefore, 5cos(1/2 t)=0 so i thought you multiply by 2 to get rid of the half then divide by 10 so the Right hand side= 0 and then inverse cos of 0 = 1/2 Pi but the answer in the textbook gives Pi.
Please help me any body!
 
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  • #2


You've got the steps right, just note that it's 1/2t = arc cos 0 and not t = arc cos 0.
 
  • #3


ohhh yeah of course! thank you very much =]
 

FAQ: Solving Differentiation Help: Find Time When Acceleration = 0

What is differentiation?

Differentiation is a mathematical process used to determine the rate of change of a function. It involves finding the derivative of a function, which gives us the slope of the tangent line at any point on the function.

How do you solve for differentiation?

To solve for differentiation, we use the rules of differentiation, which include the power rule, product rule, quotient rule, and chain rule. These rules help us find the derivative of a function by manipulating its components.

What does it mean when acceleration equals 0?

When acceleration equals 0, it means that the rate of change of velocity is constant. This can happen when an object is moving at a constant speed, or when its velocity is not changing over time.

How do you find the time when acceleration equals 0?

To find the time when acceleration equals 0, we can use the equation a(t) = 0, where a(t) represents the acceleration at a given time t. We can solve for t by setting the acceleration to 0 and solving for t using algebraic methods.

Why is it important to find the time when acceleration equals 0?

Finding the time when acceleration equals 0 can help us understand the motion of an object. It can indicate when an object is moving at a constant speed or when it is changing direction. This information is important in many scientific fields, including physics and engineering.

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