What would be the travel time from Earth orbit to Mars and Mars to Jupiter while accelerating at 3g and 5g (to a top speed of 1% light speed), braking halfway between each transit point?
3 g's is about 30 meters/sec^2 or about .03/km/sec^2. Light speed is about 300,000 km/s. .01 c is 3000 km/s. So it would take about 100,000 seconds to reach .01 c. That's about 28 hours.
With constant acceleration along the same direction, distance traveled is .5at^2. this works out to about 150,000,000 km or about 1 A.U.
Distance between earth and Jupiter can range from 4.2 to 6.2 A.U. I'll go with 4.2 A.U. So if you cut off your rocket engines after accelerating for 1 A.U., you get to coast for 2.2 A.U. At .01 c, it takes 30 hours to travel this distance.
Then the final leg you decelerate for 28 hours over which time you move 1 A.U.
Time to accelerate is 28 hours, coasting time is 30 hours, deceleration time is 28 hours. A total of 86 hours, a little less than 4 days.
Minimum distance between Earth and Mars is about .5 A.U.
Earth to Mars would be about 28 hours.
If my arithmetic's right.