- #1

MichaelTam

- 93

- 6

- Homework Statement
- MIT pretest.

- Relevant Equations
- 𝐅⃗=−𝑏𝑒^(𝑐𝑣)𝐢̂ , find v(t), by using differential equation of F=ma

There ‘s an equation, I think it should like a “drag factor” because the -(b) now has a negative symbol, which means it should be affecting the particle going parallel of the x-axis to the right, I suppose F=ma need to be apply into this equation, but before this, I need to get it into a differential equation first, but I don’t know how to isolate the exponential element, what I know is to give natural log to them , but the next step I don’t know how to do.

A particle of mass 𝑚 moving parallel to the x-axis is acted on by a velocity dependent force directed against its motion. The force is given by:

where 𝑏 is a positive constant (units N), 𝑐 ia also a positive constant (units s·m−1), and 𝑣 is the speed, the magnitude of the particle's velocity (units m·s−1).

If at 𝑡=0, the particle is moving with speed 𝑣0. Find the speed 𝑣(𝑡) as a function of time 𝑡. Express your answer in terms of some or all of the following: 𝑏, 𝑚, 𝑡, 𝑐, and v_0 for 𝑣0. Use ln() for the natural logarithm function and e^() for the exponential function if needed.

This problem I can’t reach the solution have two main reason, the first is , I get too few knowledge of exponential equation (mathematical problem) and I still feel confuse about the equation of how to derive it with an exponential element in the equation in order to get the differential equation and substitute the v(t).

A particle of mass 𝑚 moving parallel to the x-axis is acted on by a velocity dependent force directed against its motion. The force is given by:

𝐅⃗=−𝑏𝑒^(𝑐𝑣)𝐢̂ |

If at 𝑡=0, the particle is moving with speed 𝑣0. Find the speed 𝑣(𝑡) as a function of time 𝑡. Express your answer in terms of some or all of the following: 𝑏, 𝑚, 𝑡, 𝑐, and v_0 for 𝑣0. Use ln() for the natural logarithm function and e^() for the exponential function if needed.

This problem I can’t reach the solution have two main reason, the first is , I get too few knowledge of exponential equation (mathematical problem) and I still feel confuse about the equation of how to derive it with an exponential element in the equation in order to get the differential equation and substitute the v(t).

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