The position of an object moving along a line is given by #p(t) = 3t - tcos(( pi )/3t) #. What is the speed of the object at #t = 5 #?
The speed is the first derivative:
By signing up, you agree to our Terms of Service and Privacy Policy
To find the speed, calculate the absolute value of the derivative of the position function and then substitute t = 5.
[ |p'(t)| = |3 + \frac{\pi}{3} \sin\left(\frac{\pi}{3t}\right)| ]
[ \text{Speed at } t = 5: |p'(5)| ]
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- A projectile is shot from the ground at a velocity of #1 ms^-1# at an angle of #pi/3#. How long will it take for the projectile to land?
- The position of an object moving along a line is given by #p(t) = sin(2t- pi /3) +2 #. What is the speed of the object at #t = (2pi) /3 #?
- A ball rolls horizontally off a table of height 1.4 m with a speed of 4 m/s. How long does it take the ball to reach the ground?
- If a projectile is shot at an angle of #(pi)/8# and at a velocity of #13 m/s#, when will it reach its maximum height?
- What is the speed of an object that travels from #( 2,-5,6 ) # to #( 2, -4 ,1 ) # over #2 s#?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7