All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
ACT Exam  >  ACT Questions  >  The velocity of a ship varies with time as v ... Start Learning for Free
The velocity of a ship varies with time as v = 5t3. What is the acceleration at t = 2?
  • a)
    60
  • b)
    56
  • c)
    40
  • d)
    100
Correct answer is option 'A'. Can you explain this answer?
Clear all your ACT doubts with EduRev
Verified Answer
The velocity of a ship varies with time as v = 5t3. What is the accele...
Acceleration of a body can be found out by differentiating the expression for velocity. Here v = 5t3. On differentiating, a = dv/dt = 15t2. On putting t = 2, we get a = 60 units.
View all questions of this test
Most Upvoted Answer
The velocity of a ship varies with time as v = 5t3. What is the accele...
Given:
The velocity of a ship varies with time as v = 5t^3.

To find:
The acceleration at t = 2.

Acceleration:
Acceleration (a) is the rate of change of velocity with respect to time. Mathematically, it is the derivative of velocity with respect to time.

Derivative of velocity:
To find the derivative of velocity, we differentiate the given equation with respect to time (t).

Step 1:
Differentiate the given equation v = 5t^3 with respect to t using the power rule of differentiation.

dv/dt = d/dt (5t^3)
dv/dt = 15t^2

Step 2:
Substitute t = 2 into the derivative to find the acceleration at t = 2.

a = 15(2)^2
a = 15(4)
a = 60

Answer:
Therefore, the acceleration at t = 2 is 60. Hence, the correct answer is option A.
Explore Courses for ACT exam

Similar ACT Doubts

Directions:Read the passages and choose the best answer to each question.PassageNear the end of the 19th century, British engineer Osborne Reynolds ran a set of experiments to observe and predict the transition between laminar (steady) and turbulent flow of a liquid through a pipe. In Reynolds’ experiments, dye was forced through a liquid to show visually when the flow changed from laminar to turbulent. Laminar flow is common only in cases in which the flow channel is relatively small, the fluid is moving slowly, and its viscosity (the degree to which a fluid resists flow under an applied forc e) is relatively high. In turbulent flow, the speed of the fluid at any given point is continuously undergoing changes in both magnitude and direction. Reynolds demonstrated that the transition from laminar to turbulent flow in a pipe depends upon the value of a mathematical quantity equal to the velocity of flow (V ) times the diameter of the tube (D) times the mass density (ρ) of the fluid divided by its absolute viscosity (µ). The “Reynolds number,” as it is called, is determined by the following equation:Several students designed similar experiments to observe flow rates of different liquids. To conduct the experiments, the students were given the following apparatus: Liquid supply tank with clear test section tube and ‘bell mouth’ entrance 1 Rotameter to measure the velocity of flow (flow rate) Tap water • Motor oil 4, 10-ft long smooth pipes of various diameters: 0.25-inch, 0.50-inch, 0.75-inch, 1.0-inchFigure 1 illustrates an approximation of the set-up of each experiment.Figure 2 shows approximate viscosities of the water and motor oils used in the experiments.Experiment 1In Experiment 1, students began with a pipe of diameter 0.25 inches. The pipe was set first at a 15° angle and tap water was released steadily from the tank into the pipe. The velocity of flow (V) was measured. The pipe was then set at a 30° angle, a 45° angle, and a 60° angle, water was released steadily from the tank into the pipe, and the velocity of flow was measured. The process was then repeated for each diameter of pipe using the same amount of water each time. All data were recorded in Table 1. Temperature of the water was held constant at 20°C.Experiment 2In the second experiment, the tap water was replaced by Motor Oil A and the processes were repeated. The results are given in Table 2.Experiment 3In a third experiment, the tap water was replaced by Motor Oil B and the processes were repeated.Q.Based on Experiment 1, the relationship between the angle of the pipe and the velocity of flow

Top Courses for ACTView all

Top Courses for ACT

The velocity of a ship varies with time as v = 5t3. What is the acceleration at t = 2?a)60b)56c)40d)100Correct answer is option 'A'. Can you explain this answer?
Question Description
The velocity of a ship varies with time as v = 5t3. What is the acceleration at t = 2?a)60b)56c)40d)100Correct answer is option 'A'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about The velocity of a ship varies with time as v = 5t3. What is the acceleration at t = 2?a)60b)56c)40d)100Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The velocity of a ship varies with time as v = 5t3. What is the acceleration at t = 2?a)60b)56c)40d)100Correct answer is option 'A'. Can you explain this answer?.
Solutions for The velocity of a ship varies with time as v = 5t3. What is the acceleration at t = 2?a)60b)56c)40d)100Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for ACT. Download more important topics, notes, lectures and mock test series for ACT Exam by signing up for free.
Here you can find the meaning of The velocity of a ship varies with time as v = 5t3. What is the acceleration at t = 2?a)60b)56c)40d)100Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The velocity of a ship varies with time as v = 5t3. What is the acceleration at t = 2?a)60b)56c)40d)100Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The velocity of a ship varies with time as v = 5t3. What is the acceleration at t = 2?a)60b)56c)40d)100Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The velocity of a ship varies with time as v = 5t3. What is the acceleration at t = 2?a)60b)56c)40d)100Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The velocity of a ship varies with time as v = 5t3. What is the acceleration at t = 2?a)60b)56c)40d)100Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice ACT tests.
Explore Courses for ACT exam

Top Courses for ACT

Explore Courses
SaveJoin the Discussion on the App for FREE
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup