Lead researcher Dr Erica Camargo said this level of testing could be routinely carried out by primary care physicians and GPs. "These are basic office tests which can provide insight into risk of dementia and stroke and can be easily performed by a neurologist or general practitioner," she added.
Participants in the US study were tested for walking speed, hand grip strength and cognitive function, and had brain scans.
During the follow-up period, 34 people developed dementia and 70 people had a stroke.
Dr Camargo, of Boston Medical Centre, said: "While frailty and lower physical performance in elderly people have been associated with an increased risk of dementia, we weren't sure how it impacted people of middle age."
Researchers also found that slower walking speed was associated with lower total cerebral brain volume - fewer "grey" cells and poorer performance on memory, language and decision-making tests. Stronger grip strength was associated with larger total cerebral brain volume as well as better performance on cognitive tests asking people to identify similarities among objects.
"Further research is needed to understand why this is happening and whether preclinical disease could cause slow walking and decreased strength," added Dr Camargo.
Dr Anne Corbett, of the Alzheimer's Society, said: "Before people take stock in the strength of a handshake or the speed you cross the road, more research is needed to understand why and what other factors are involved.
"The good news is that there are many things to reduce your risk of developing dementia.
"We recommend you eat a healthy balanced diet, don't smoke, maintain a healthy weight, take regular exercise, and get your blood pressure and cholesterol checked regularly."
The research was presented yesterday at the American Academy of Neurology's 64th annual meeting in New Orleans. Some 820,000 people are affected by dementia in the UK.
- DAILY MAIL